I have never been able to find a source verifying that this picture is authentic. Here is a bit of background. The Beethoven-Haus in Bonn, an authoritative source, gives a picture of an engraving (black and white) that looks rather like this picture. They say it is an engraved portrait made by Riedel "based on an earlier drawing from Vienna portrait artist Gandolph Ernst Stainhauser." You can see this engraving at their website: [1] (and we have a copy of it here on the Commons; see above).

The image above is colored -- who did this? -- and I think it is also much more flattering than the engraving displayed by the Beethoven-Haus (wide eyes, trimmed eyebrows, little smile, rosy cheeks). Could it be a long-post-Beethoven sentimentalized version of the Riedel engraving? Certainly there is precedent for this kind of falsification. And the hypothesis that it is a post-lifetime sentimentalized portrait would explain why it displays a handsome young man when contemporary testimony (see Beethoven-Haus link) tells us that Beethoven was quite ugly.